Can you let me know which parameter exactly are you talking about?
I've just tested "Gui Skin \ Button \ Text Padd" in the Gui Skin Editor, and applied this skin to a button in the Gui Editor, and padding works as expected.
Make sure your button actually uses this skin, or it's the default skin of your application (and the button doesn't override the default skin).
You have to control the button alignment in the Gui Editor, in the Button properties (not in the Gui Skin Editor).
Or through code using Button.text_align;
This setting is controlled for each button separately, so you can't change it globally for all buttons.
By default the alignment is centered, so adjusting the padding won't make a difference (because of center alignment).
You will see a difference in padding once you change alignment.